Division: Laying the Groundwork, Part 3

Manipulatives make learning fun.
Manipulatives make learning fun.

 Laying the Groundwork for Teaching Division, Part3

In Part 1 and Part 2 of Laying the Groundwork for Teaching Division, I discussed ways parents can begin laying the groundwork for the future teaching of division to their children.

Teaching division may seem like a complicated task but using manipulatives makes the skill easy to teach and to acquire.

For our purposes in this post, we will use recycled ice cream sticks. Family members could assist in recycling so that you have a useful amount.

Ask extended family members to save items that can be used as manipulatives to teach mathematical skills.
Ask extended family members to save items that can be used as manipulatives to teach mathematical skills.

(Another alternative would be to use tongue depressors. Just ask your doctor for a handful next time you have an appointment. If you tell him or her the purpose for your request, you may find yourself with a generous handful free of charge.)

Let’s Review Place Value First

Before we continue let’s take a moment to discuss the place value of numbers. This is just for the parents’ information.

The number 2 is a one-digit number which is made up of 2 one’s.

The number 23 is a two-digit number which is made up of 2 tens and 3 ones.

The number 234 is a three-digit number which is made up of 2 hundreds, 3 tens, and 4 ones.

In the number 2, the digit 2 is in the one’s place.

In the number 23, the digit 2 is in the ten’s place.

In the number 234, the digit 2 is in the hundred’s place.

In other words, a 3-digit number has 3 digits, one which represents the hundred’s place, one which represents the ten’s place, and one which represents the one’s place.

In the number 2, there is only one digit. This tells us we have 2 ones.

In the number 23, there are two digits. This tells us we have 2 tens and three ones.

In the number 234, there are three digits. This tells us we have 2 hundreds, 3 tens, and 4 ones.

Prepare Your Manipulatives
Choose your colors.

Back to our ice cream sticks. Choose a color you wish to use to represent the hundred’s place. For our demonstration we will use purple.

Choose another color to represent the ten’s place. For our demonstration we will use red.

Now choose another color to represent the one’s place. For our demonstration we will use yellow.

Use markers, paints, crayons, etc., per your color choices

Use markers, paints, or crayons according to your color choice to dye your assortment of ice cream sticks.  If your budget allows, colored ice cream sticks may be purchased inexpensively at various craft stores.

Teaching the Skill of Division Using Your Manipulatives

Now that you have your own manipulatives, let’s see how we can use them to continue laying the groundwork for teaching the concepts of division. You will find it much easier than you thought.

Ice cream sticks may be used to represent numbers.
Ice cream sticks may be used to represent numbers.
To represent the number 234, we will use 2 purple sticks, 3 red sticks, and 4 yellow sticks (per our color choices).

(To make this task even easier, you may decide to only use even numbers for all digits, especially if your child/student is very young.)

234/2 = ____
The example problem we will be solving is 234 divided by 2.
  • Lay the sticks out in proper order to represent the number 234.
Place value represented by manipulatives
Representing place value
Explain to your child what the colors represent.
  • Explain to your child what the colors represent. Always use the same colors to represent the same place value.
  • Tell your child to “pretend” he or she has two friends. The number 234 can represent marbles, cookies, building blocks, or whatever your child likes to play with.
  • Tell your child to divide the 234 between his or her two pretend friends equally.
Direct them through the process.

Draw attention to the 2 “hundred’s” sticks (purple). Share these two sticks equally.  They will place one stick in each pretend friend’s pile.

The “hundreds” divided.

Then direct them to divide the three “ten’s” sticks (red). They will place one stick in each pretend friend’s pile. But what will they do with the third stick? No, they cannot break it.

Problem represented thus far

Show them that they can solve this by trading the “ten” stick for ten “ones” sticks.

Now show them to place the ten “ones” sticks with the 4 “ones” sticks. How many “one” sticks (yellow) do they have now?

Ask them to divide these 14 “ones” sticks between the two “pretend” friends. 7 “ones” sticks should be placed in each pretend friend’s pile.

7 yellow sticks go to each friend
Explain the answer to the problem.

234 has now been divided into two equal but separate groups. The answer to the problem is the amount in one of the groups.

  • So, if we share 234 building blocks equally between two friends, each friend will have 117 blocks.

Therefore, 234 divided by 2 is 117.

234 divided equally between 2 friends.
234 divided equally between two friends.

This is an example of the division of a three-digit number by a one-digit number.

Where to start
  • Begin with the division of a one-digit number by a one-digit number, continue with the division of two-digit numbers by a one-digit number, and then the division of three-digit numbers by a one-digit number.
  • Go at your child’s pace.

Remember this is to be a time of enjoyment. Don’t get stressed if your child struggles at first. Eager learners will pick up on what you are requesting as you continue along.

I do hope these posts have been helpful. Parents can do a tremendous job of helping their children enjoy learning these somewhat difficult tasks.

Just take a few minutes each day to lay the groundwork for division and your child will find this task conquerable.

You may leave any questions in the comment box below.

Copyright 2017 by Peggy Clark

 

 

Be an Effective Teacher Without the Frustration

Sometimes we have a struggler who just doesn't seem to get the lesson we're trying to present no matter how many times we have presented it. Frustration may try to overtake us but we must not allow it to take us captive to its destructive vice.

Instead we must find another way to present the lesson that is geared toward our child's learning style and learning ability.

A greater time may need to be spent on teaching the concept. Let's face it. Do we always grasp how to do something the first time we see or hear the instructions? We must remember to teach effectively, not hurriedly. 

Use manipulatives whenever possible. Manipulatives are objects, drawings, charts, number lines, or other tools that a child may touch, handle, and manipulate. For example, instead of trying to describe how to do an addition equation, picture the process first.

Draw the addition problem on the page. 
9 + 8 = ? 
Draw a set of 9 triangles and a set of 8 triangles. 
Then circle both sets to show that you are going to group them together. Let the child give the answer.

Next use objects to show the equation process. 
Place 9 objects in one group. Place 8 objects in another group. Then pull the objects into one group. Let the child give the answer.

Then have the child use the objects to show the equation process using the same equation. If he or she does this correctly, then give the child another equation. 

7 + 5 = ?
Let the child use the objects to show the equation process. 7 objects should be placed in one group. 5 objects should be placed in another group. Allow the child to explain what he or she is doing so you can see if they are processing the problem correctly. Let the child give the answer to the equation. 

When you are satisfied that the process has been understood correctly, go back to paper and do several equations together if necessary. 

Stay focused on the goal of the lesson. Teach the lesson effectively without frustration. An effective teacher will seem to overteach at times but the goal of understanding will be achieved at a higher rate. And is understanding not what we're trying to achieve?


For precept must be upon precept, precept upon precept; line upon line, line upon line; here a little, and there a little. Isaiah 28:10